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Chapters

Spectral Audio Signal Processing
    Beginning Statistical Signal Processing
       Random Variables & Stochastic Processes
          Variance

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Variance



Definition: The variance or second central moment of a stochastic process $ v(n)$ at time $ n$ is defined as the expected value of $ \left\vert v(n)-\mu_{v(n)}\right\vert^2$:

$\displaystyle \sigma^2_{v(n)} \isdef E\{\left\vert v(n)-\mu_{v(n)}\right\vert^2... ...f \int_{-\infty}^\infty \left\vert v(n)-\mu_{v(n)}\right\vert^2 p_{v(n)}(x) dx $

where $ p_{v(n)}(x)$ is the probability density function for the random variable $ v(n)$.

For a stationary stochastic process $ v$, the variance is given by the expected value of $ \left\vert v(n)-\mu_v\right\vert^2$ for any $ n$.

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


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